Three-Dimensional Simulations of the Jeans-Parker Instability

We have studied the nonlinear evolution of a magnetized disk of isothermal gas, which is sustained by its self-gravity. Our objective is to investigate how the Jeans, Parker, and convective instabilities compete with each other in structuring/de-structuring large scale condensations in such disk. The Poisson equation for the self-gravity has been solved with a fourth-order accurate Fourier method along with the Green function, and the MHD part has been handled by an isothermal TVD code. When large wavelength perturbations are applied, the combined action of the Jeans and Parker instabilities suppresses the development of the convection and forms a dense core of prolate shape in the mid-plane. Peripheral structures around it are filamentary. The low density filaments connect the dense core to the diffuse upper region. On the other hand, when small wavelength perturbations are applied, the disk develops into an equilibrium state which is reminiscent of the Mouschovias's 2-D non-linear equilibrium of the classical Parker instability under an externally given gravity.